The present disclosure relates to the acceleration of lossless compressed data transfers between data memories having different access times and particularly the movement of large matrices between memories of different access timing. Without limitation, this matrix compression accelerator (MCA) may be applied to situations where very large convolutional neural network (CNN) feature maps may be transferred between external data memory (EDM) under control of a digital central processing unit (CPU) or other application control logic (ACL) and local data memory (LDM) within the control of an integrated matrix compute engine (MCE) in which matrix computation operators (MCO) may be applied to tiled matrix data (TMD) contained within the LDM.